Question

Write and solve the equation and then check your answer. Select the correct statements for each blank.

A number decreased by sixty-eight is thirty-one.



(5 points)
Equation: ____

This is a _____ problem.

To solve the equation, _____ ___ to both sides of the equation.

To check the solution, ______ 99 for the variable in the equation.

Answer 1

Let's break down the problem step by step.

1. **Equation**: We need to write an equation based on the statement: "A number decreased by sixty-eight is thirty-one." If we let the variable \( x \) represent the unknown number, the equation would be:
\[
x - 68 = 31
\]

2. **This is a**: The problem is a **subtraction** problem, since it involves decreasing a number (subtracting).

3. **To solve the equation,** we need to **add 68** to both sides of the equation. The adjustment will isolate \( x \):
\[
x - 68 + 68 = 31 + 68
\]
\[
x = 99
\]

4. **To check the solution,** we need to **substitute** 99 for the variable in the equation. We can verify by plugging the value back into the original equation:
\[
99 - 68 = 31
\]
Simplifying it gives:
\[
31 = 31
\]
This confirms that our solution is correct.

Now let's fill in the blanks:

- Equation: **x - 68 = 31**
- This is a **subtraction** problem.
- To solve the equation, **add 68** to both sides of the equation.
- To check the solution, **substitute** 99 for the variable in the equation.